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An In-Depth Look at the Madelung Constant for Cubic Crystal Systems

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Robert P. Grosso Jr., Justin T. Fermann and William J. Vining

Department of Chemistry, University of Massachusetts, Amherst, MA 01003-4510

J. Chem. Educ., 2001, 78 (9), p 1198

DOI: 10.1021/ed078p1198

Publication Date (Web): September 1, 2001

Section:

History, Education, and Documentation

Abstract

The way in which the Madelung constant is presented to undergraduate chemistry students provides little insight into its meaning. Students are usually shown the first six terms of the sodium chloride Madelung series and told that the series is infinite and takes into account all electrostatic interactions of the ions arranged in that structure. There is usually little discussion of how the series is generated and what each term represents. This paper presents an in-depth look at the Madelung constant for cubic crystal systems. We show how the numerators of the terms of the series refer to multiplicities of x,y,z positions in space and how these multiplicities can be calculated. We also show how to transfer this method of generating the Madelung series from orthogonally bonded sodium chloride to other cubic systems such as cesium chloride and zinc blende. Convergence of the series is discussed, establishing that the condition of charge neutrality is crucial in getting the Madelung series to converge.

Keywords (Audience):

Second-Year Undergraduate

Keywords (Domain):

Inorganic Chemistry

Keywords (Pedagogy):

Computer-Based Learning

Keywords (Subject):

Atomic Properties / Structure

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Citing Articles

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This article has been cited by 3 ACS Journal articles (3 most recent appear below).

Teaching Nanochemistry: Madelung Constants of Nanocrystals
Mark D. Baker, A. David Baker
Journal of Chemical Education2010 87 (3), 280-284
- Teaching Nanochemistry: Madelung Constants of Nanocrystals
  Mark D. Baker, A. David Baker
  Journal of Chemical Education2010 87 (3), 280-284
  The Madelung constants for binary ionic nanoparticles are determined. The computational method described here sums the Coulombic interactions of each ion in the particle without the use of partial charges commonly used for bulk materials. The results show ...
  Abstract | Full Text HTML | Hi-Res PDF | PDF w/ Links
A Simple Spreadsheet Program for the Calculation of Lattice-Site Distributions
John G. McCaffrey
Journal of Chemical Education2009 86 (12), 1450
- A Simple Spreadsheet Program for the Calculation of Lattice-Site Distributions
  John G. McCaffrey
  Journal of Chemical Education2009 86 (12), 1450
  A simple spreadsheet program is presented that can be used by undergraduate students to calculate the lattice-site distributions in solids. A major strength of the method is the natural way in which the correct number of ions or atoms are present, or ...
  Abstract | Hi-Res PDF | PDF w/ Links
Madelung Constants of Nanoparticles and Nanosurfaces
A. D. Baker and M. D. Baker
The Journal of Physical Chemistry C2009 113 (33), 14793-14797
- Madelung Constants of Nanoparticles and Nanosurfaces
  A. D. Baker and M. D. Baker
  The Journal of Physical Chemistry C2009 113 (33), 14793-14797
  Specific ion Madelung Constants (MCs) were calculated for ionic nanostructures and nanosurfaces using Coulomb sums. The magnitude of these values was tracked through a succession of progressively larger structures having the same symmetry. A significantly ...
  Abstract | Full Text HTML | Hi-Res PDF | PDF w/ Links